Advances in Mathematical Systems Theory

1 Transitory Behavior of Uncertain Systems.- 1.1 Introduction.- 1.2 Transient Excursions.- 1.3 Pseudospectra and Spectral Value Sets.- 1.4 State Feedback.- 1.5 Transient Excursions of Uncertain Systems.- 2 Robust Stability of Multivariate Polynomials.- 2.1 Introduction.- 2.2 Basic Notions and Definitions.- 2.2.1 Classes of Stable Polynomials.- 2.3 Properties of Stable Polynomials.- 2.4 Zero Exclusion Principle.- 3 Robustness of Nonlinear Systems and Their Domains of Attraction.- 3.1 Introduction.- 3.2 Preliminaries.- 3.3 Linearization Theory.- 3.4 Calculating the Local Stability Radius.- 3.5 Robust Domains of Attraction.- 3.6 An Optimal Control Characterization of the Robust Domain of Attraction.- 3.7 Conclusion.- 4 On Stability Radii of Slowly Time-Varying Systems.- 4.1 Introduction.- 4.2 Perturbation Classes.- 4.3 Stability of Nonlinearly Perturbed Linear Systems.- 4.4 Stability Radii of Slowly Time-Varying Systems.- 4.5 Two Lemmas.- 4.6 Conclusions.- 5 An Invariance Radius for Nonlinear Systems.- 5.1 Introduction.- 5.2 Background on Invariant Control Sets and Chain Control Sets.- 5.3 An Invariance Radius for Nonlinear Systems.- 6 State and Continuity.- 6.1 Introduction.- 6.2 Linear Differential Systems.- 6.3 Latent Variables.- 6.4 State Representations.- 6.5 Smoothing Functionals.- 6.6 Main Results.- 6.7 Proofs.- 6.8 Remarks.- 7 Parameterization of Conditioned Invariant Subspaces.- 7.1 Introduction.- 7.2 Preliminaries.- 7.3 On Conditioned Invariant Subspaces.- 7.4 The State Space Approach.- 7.5 On the Parameterization of Conditioned Invariant Subspaces.- 7.6 Topology of Tight Conditioned Invariant Subspaces.- 7.7 Brunovsky Strata for Conditioned Invariant Subspaces...- 8 Duality Between Multidimensional Convolutional Codes and Systems.- 8.1 Introduction.- 8.2 Multidimensional Convolutional Codes.- 8.3 Duality Between Codes and Behaviors.- 8.4 First-Order Representations for One-Dimensional Codes.- 8.5 Conclusion.- 9 Control of Rate-Bounded Hybrid Systems with Liveness Constraints.- 9.1 Introduction.- 9.2 Hybrid Machines.- 9.3 Liveness.- 9.4 Control.- 10 A General Principle of Marked Extraction.- 10.1 Introduction.- 10.2 Joint Production and the Substitution Theorem.- 10.3 Marked Extraction in Convex Sets.- 10.4 The Factorial Complex of a Krull Monoid.- 11 Between Mathematical Programming and Systems Theory: Linear Complementarity Systems.- 11.1 Introduction.- 11.2 Examples.- 11.3 Existence and uniqueness of solutions.- 11.4 Linear complementarity systems.- 11.5 A distributional interpretation.- 11.6 Well-posedness.- 11.7 Relay systems.- 11.8 Discontinuous dependence on initial conditions.- 11.9 Conclusions.- 12 Exact Controllability of Co-groups with One-Dimensional Input Operators.- 12.1 Introduction.- 12.2 System Description.- 12.3 Exact Controllability.- 12.4 Proofs of the Main Results.- 12.5 An Example.- 13 Normalized Coprime Factorizations for Strongly Stabilizable Systems.- 13.1 Introduction.- 13.2 Problem Formulation and Mathematical Background.- 13.3 Formulae for Normalized Coprime Factorizations.- 13.4 Application to Hybrid Flexible Structures.- 14 Low-Gain Integral Control of Infinite-Dimensional Regular Linear Systems Subject to Input Hysteresis.- 14.1 Introduction.- 14.2 Preliminaries on Regular Linear Systems.- 14.3 A Class of Causal Monotone Nonlinear Operators.- 14.4 Integral Control in the Presence of Input Nonlinearities Satisfying (N1) to (N8).- 14.5 Hysteresis Nonlinearities Satisfying (N1) to (N8).- 14.6 Example: Controlled Diffusion Process with Output Delay.- 14.7 Appendix.